Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
616 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 274 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×#6923 |
| commutator | C2×C61 | C23×C8 |
| Frattini | C22 | C23×#6923 |
| Fitting | C22×D4×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C22×D4 | #6923 |
| hypocenter | C61 | C2×C8×D4 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#92420 | C2 | semidirect |
| 2. D4×#92420 | C2 | direct (N × H) |
| 3. C2×C4⋊#92420 | C2 | semidirect |
| 4. C2×C22⋊#92420 | C2 | semidirect |
| 5. C2×C4×#92420 | C2 | semidirect |
| 11. C22×#92420 | C22 | semidirect |
| 12. C4⋊#92420 | C22 | semidirect |
| 13. C22⋊#92420 | C22 | semidirect |
| 14. C4×#92420 | C22 | semidirect |
| 23. C2×D4×C61 | C8 | semidirect |
| 36. C2×#92420 | D4 | direct (N × H) |
| 46. C23×C61 | C2×C8 | semidirect |
| 49. D4×C61 | C2×C8 | semidirect |
| 50. C2×C4×C61 | C2×C8 | semidirect |
| 65. #92420 | C2×D4 | direct (N × H) |
| 71. C22×C61 | C22×C8 | semidirect |
| 74. C4×C61 | C22×C8 | semidirect |
| 82. C2×C61 | C8×D4 | semidirect |
| 92. C61 | C2×C8×D4 | semidirect |
| 109. C2×D4 | #92420 | direct (N × H) |
| 132. C23 | C2×#92420 | semidirect |
| 135. D4 | C2×#92420 | direct (N × H) |
| 147. C2×C4 | C2×#92420 | semidirect |
| 157. C22 | C22×#92420 | semidirect |
| 165. C4 | C22×#92420 | semidirect |
| 167. C2 | D4×#92420 | direct (N × H) |